Suppose this scenario, two orbiting stars with let's say equal masses to the sun. With both orbiting the common point, the barycentre, would gravitational time dilation occur at the barycetnre occur equally as if you were at a hypothetical point on either star?
If that's not clear I'm not sure how I can make that question clearer.
So theoretically would at the equivalent time dilation occur (or occur at all) at the barycentre?